Group Betweenness Centrality
Definition
Group betweenness centrality (GBC) shows the proportion of geodesics connecting pairs of non-group members that pass through a group of nodes.
GBC of a group of nodes stands for the fraction of shortest paths between pairs of nodes in a network that passes through at least one of the nodes in the group. Thus, GBC can be used for estimating the ability of a group of collaborating nodes to monitor the network traffic. [EVERETT, M. G. 1999, PUZIS, R., 2009]
Defined the group betweenness of u and v as:
where:
for i1, i2 ∈ {u, v}, and σst (i1, i2) is the number of geodesic paths
between vertices s and t that pass through both i1 and i2.
[KOLACZYK, E. D., 2009]
GBC of a group of nodes stands for the fraction of shortest paths between pairs of nodes in a network that passes through at least one of the nodes in the group. Thus, GBC can be used for estimating the ability of a group of collaborating nodes to monitor the network traffic. [EVERETT, M. G. 1999, PUZIS, R., 2009]
Defined the group betweenness of u and v as:
B(u, v) = C{u,v}(u, u) + C{u,v}(v, v) − C{u,v}(u, v),
[KOLACZYK, E. D., 2009]
Faster computation of successive bounds on the group betweenness centrality
Dinler, D. and Tural, M.K., Faster computation of successive bounds on the group betweenness centrality. Networks - Wiley Online Library.
K-step Group Betweenness Centrality
Akgün, M.K. and Tural, M.K., 2020. k-step betweenness centrality. Computational and Mathematical Organization Theory, 26(1), pp.55-87.
Software
References
- EVERETT, M. G. & BORGATTI, S. P. 1999. The centrality of groups and classes. Journal of Mathematical Sociology, 23, 181-201.
DOI: 10.1080/0022250X.1999.9990219
- KOLACZYK, E. D., CHUA, D. B. & BARTHÉLEMY, M. 2009. Group betweenness and co-betweenness: Inter-related notions of coalition centrality. Social Networks, 31, 190-203.
DOI: 10.1016/j.socnet.2009.02.003
- PUZIS, R., YAGIL, D., ELOVICI, Y. & BRAHA, D. 2009. Collaborative attack on Internet users' anonymity. Internet Research, 19, 60-77.
DOI: 10.1108/10662240910927821